Download A Panorama of Hungarian Mathematics in the Twentieth by Janos Horvath PDF

By Janos Horvath

An excellent interval of Hungarian arithmetic began in 1900 whilst Lipót Fejér came across the summability of Fourier series.This was once by way of the discoveries of his disciples in Fourier research and within the thought of analytic features. whilst Frederic (Frigyes) Riesz created practical research and Alfred Haar gave the 1st instance of wavelets. Later the themes investigated through Hungarian mathematicians broadened significantly, and integrated topology, operator thought, differential equations, likelihood, and so on. the current quantity, the 1st of 2, offers probably the most awesome effects accomplished within the 20th century through Hungarians in research, geometry and stochastics. The publication is obtainable to somebody with a minimal wisdom of arithmetic. it really is supplemented with an essay at the heritage of Hungary within the 20th century and biographies of these mathematicians who're now not energetic. a listing of all individuals pointed out within the chapters concludes the amount.

This quantity comprises contributions by means of contributors within the AMS-IMS-SIAM summer season learn convention on Hamiltonian Dynamical structures, held on the college of Colorado in June 1984. The convention introduced jointly researchers from a large spectrum of parts in Hamiltonian dynamics. The papers fluctuate from expository descriptions of modern advancements to relatively technical displays with new effects.

A textbook for collage scholars (physicists and mathematicians) with precise supplementary fabric on mathematical physics. in accordance with the path learn by means of the writer on the Moscow Engineering Physics Institute. quantity 2 comprises a number of integrals, box thought, Fourier sequence and Fourier necessary, differential manifolds and differential kinds, and the Lebesgue critical.

Paul Butzer, who's thought of the educational father and grandfather of many favourite mathematicians, has validated the best faculties in approximation and sampling idea on the earth. he's one of many best figures in approximation, sampling idea, and harmonic research. even supposing on April 15, 2013, Paul Butzer grew to become eighty five years previous, remarkably, he's nonetheless an lively study mathematician.

Extra resources for A Panorama of Hungarian Mathematics in the Twentieth Century, I

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Lakl ~ ... be a decreasing rearrangement of the sequence (ak) of numbers. e. if and only if L L 00 p=O { lakf(log k)2 }1/2 < 00 . kElp The idea of studying unconditional convergence is due to Wladislaw Orlicz {12}, who proved the first basic result in this direction. His result , which is actually a consequence of the above theorem of Tandori, is formulated in terms of the so-called Weyl multiplier. 52 F. M6ricz Corollary. Let (A(k) : k = 1,2 , ... ) be an increasing sequence of positive numbers.

Orthogonal Series A 21f-periodic function I is said to satisfy the uniform Lipschitz condition of order a > 0, in symbol: I E Lip21r a, if Only the case 0 < a :S 1 is interesting: if a > 1, then w(f,o)/o tends to zero with o. Consequently, in this case f'(x) exists and is zero everywhere, and I is constant. The function w(f, 0), 0 :S 0 < 21f, is called the modulus of continuity of I. It is clear that a function I is uniformly continuous if and only if w(f, 0) tends to zero with o. On the other hand, I belongs to LiP21r 1 if and only if I is the antiderivative of a bounded function .